A%20Hybrid%20Test%20Compression%20Technique%20for%20Efficient%20Testing%20of%20Systems-on-a-Chip

1
A Hybrid Test Compression Technique for Efficient
Testing of Systems-on-a-Chip

• Aiman El-Maleh
• King Fahd University of Petroleum Minerals,
  Dept. of Computer Eng., Saudi Arabia

2
Outline

• Motivation
• Test compression techniques
• Geometric Shapes Compression Technique
• FDR Compression Technique
• EFDR Compression Technique
• Hybrid Compression Technique
• Experimental results
• Conclusions

3
Motivation

• With todays technology, complete systems with
  millions of transistors are built on a single
  chip
• Increasing complexity of systems-on-a-chip and
  its test data size increased cost of testing
• Test data must be stored in tester memory and
  transferred from tester to chip
• Cost of automatic test equipment increases with
  increase in speed, channel capacity, and memory.
• Need for test data reduction is imperative
• Test compaction
• Test compression

4
Test compression techniques

• Burrows-wheeler transformation modified
  run-length coding Yamaguchi et al., ITC 97
• Statistical coding based on modified Huffman
  codes Jas et al., VTS 99
• Coding based on storing differing bits, decoding
  based on embedded processor Jas et al., ICCD 99
• Variable-to-block run-length coding, encoding
  runs of 0s followed by 1 Jas et al., ITC 98
• Variable-to-variable run-length coding using
  Golomb codes Chandra et al., VTS 2000
• Variable-to-variable run-length coding using FDR
  codes Chandra et al., VTS 2001
• Primitive Geometric shapes based Compression
  El-Maleh et al., VTS 2001
• Variable-to-variable run-length coding using EFDR
  codes El-Maleh et al., ICECS 2002

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Geometric Compression Technique Used geometric
shapes

• Point
• Lines

Type1 Type2 Type3 Type4

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Used geometric shapes- cont.

• Triangles
• Rectangle

Type1 Type2 Type3 Type4

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Geometric compression technique encoding
algorithm

• Test set sorting
• Generate clusters of 0s or 1s efficiently
  encoded by geometric shapes
• Test set partitioning
• Test set partitioned into L segments
• Each segment consists of K blocks
• Each block is NxN bits
• Block encoding
• Do not encode block and store actual test data
  (00)
• Encode block as filled with all 0s (010)
• Encode block as filled with all 1s (011)
• Encode 0s by geometric shapes (10)
• Encode 1s by geometric shapes (11)

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FDR Compression Technique

• Based on run-length coding
• A run is a consecutive sequence of equal symbols.
  
• A sequence of symbols can be encoded using two
  elements for each run
• the repeating symbol and
• the number of times it appears in the run
• A variable-to-variable coding technique based on
  encoding runs of 0s followed by a 1
• Designed based on the observation that frequency
  of runs decreases with the increase in their
  lengths.
• Assign smaller code words to runs with small
  length and larger code words to those with larger
  length

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FDR Codes

• Prefix and tail of any codeword are of equal size
  
• In any group Ai, the prefix is of size i bits.
• When moving from group Ai to group Ai1, the
  length of the code words increases by two bits

Group Run Length Group Prefix Tail Code word
A1 0 0 0 00
A1 1 0 1 01
A2 2 10 00 1000
A2 3 10 01 1001
A2 4 10 10 1010
A2 5 10 11 1011
A3 6 110 000 110000
A3 . 110 . .
A3 13 110 111 110111
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Extended FDR (EFDR) Codes

• FDR code extended by encoding both types of runs
• An extra bit is added to beginning of a code word
  to indicate type of run

Group Run Length Group Prefix Tail Code word for 0 Runs Code word for 1 Runs
A1 1 0 0 000 100
A1 2 0 1 001 101
A2 3 10 00 01000 11000
A2 4 10 01 01001 11001
A2 5 10 10 01010 11010
A2 6 10 11 01011 11011
A3 7 110 000 0110000 1110000
A3 . 110 . . .
A3 14 110 111 0110111 1110111
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Proposed Hybrid Compression Technique

• Combines Geometric compression technique with FDR
  or EFDR compression techniques
• Main objective is to reduce the number of blocks
  encoded by storing the real test data

Header Code Encoded Block
000 With real test data
001 With FDR or EFDR codes
010 As filled with 0s
011 As filled with 1s
10 With geometric shapes covering 0s
11 With geometric shapes covering 1s
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Experimental results

• Benchmark circuits
• Largest ISCAS 85 and full-scanned versions of
  ISCAS 89 circuits
• Test sets
• 14 different test sets
• Dynamic compaction by Mintest Hamzaoglu Patel,
  ICCAD 98
• Static compaction by Mintest (Relaxed)
• Compression ratio
• (Original Bits - Compressed Bits)/Original
  Bits

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Comparison with Geometric FDR Compression
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Compression results of Geometric, FDR, EFDR,
GFDR, and GEFDR
Circuit Orig. Bits Geom. FDR EFDR GFDR GEFDR
c2670 10252 51.85 43.82 53.11 54.14 54.56
s35932 21156 25.78 3.99 45.63 26.27 44.93
s38417 113152 46.5 37.66 52.35 48.37 51.45
s5378 20758 51.55 46.85 50.81 53.12 53.18
s35932d 28208 78.123 19.36 80.31 78.12 81.71
s38417d 164736 62.226 43.27 60.57 63.09 65.23
s9234d 39273 57.22 43.61 45.89 58.39 57.87
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Analysis of block encoding for Geometric, GFDR,
and GEFDR
Geometric Geometric Geometric Geometric GFDR GFDR GFDR GEFDR GEFDR GEFDR
Circuit Blk Fill Shape Encod. Real Shape Encod. FDR Encod. Real Shape Encod. EFDR Encod. Real
c2670 180 56 99 25 70 33 21 68 40 16
s35932 442 76 191 175 182 54 130 129 196 41
s38417 1872 252 1484 136 1214 348 58 1059 534 27
s5378 351 73 220 58 193 46 39 185 63 30
s35932d 442 56 384 2 384 0 2 334 50 2
s38417d 2704 1068 1447 189 1290 220 126 1129 453 54
s9234d 620 150 410 60 367 71 32 375 60 35
AVG 28.97 55.87 15.16 48.78 12.23 10.2 46.16 17.5 7.37
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Conclusions

• Proposed hybrid compression scheme that combines
  Geometric compression with FDR (GFDR) or with
  EFDR (GEFDR)
• Objective is to reduce the number of blocks
  encoded by real test data
• GEFDR (GFDR) reduced blocks encoded by real data
  from 15 to 7 (10)
• In GEFDR, Blocks encoded by Geometric are 46 and
  those encoded by EFDR are 18.
• In GFDR, Blocks encoded by Geometric are 49 and
  those encoded by EFDR are 12.
• Hybrid compression schemes performed consistently
  better than Geometric
• GEFDR achieved the best results and improved
  compression on average from 59 to 62.